# "Lorentz transformation" for general dislocation

Let's fix a coordinates system $$(x,y,z)$$ with origin $$O$$. Considering a (screw or edge) dislocation and let the coordinate system $$(x',y',z')$$ with origin $$O'$$ move with the dislocation, and impose the condition that the two origins $$O$$ and $$O'$$ coincide at $$t=0$$. Then the following transformation holds

$$\begin{array}{l}x^{\prime}=\frac{x-v t}{\left(1-v^{2} / c_{t}^{2}\right)^{1 / 2}} \\ y^{\prime}=y \\ z^{\prime}=z \\ t^{\prime}=\frac{t-v x / c_{t}^{2}}{\left(1-v^{2} / c_{t}^{2}\right)^{1 / 2}}\end{array}$$

where $$c_t$$ is the speed of sound in the given material.

Does this transformation hold for a general dislocation (e.g. a loop dislocation) or what is the general transformation from the rest frame of the material (its lattice) to the moving frame of the dislocation?

• Are you sure $c_t$ should be the speed of sound, because these transformations are valid only because of the constancy of speed of light May 19, 2020 at 23:41
• $c_t$ is the speed of sound. These transformations are also valid for uniformly moving screw and edge dislocations in a crystal. They don't have anything to do with special relativity. They look the same but describe two physically diffrent systems. May 20, 2020 at 11:26